Kitty doesn't finish having a good time (3)
I believe the answer is:
fun
'a good time' is the definition.
(I've seen this in another clue)
'kitty doesn't finish' is the wordplay.
'kitty' becomes 'fund' (fund or money for a particular purpose).
'doesn't finish' means to remove the last letter.
'fund' with its final letter removed is 'FUN'.
'having' acts as a link.
(Other definitions for fun that I've seen before include "'Merriment, playfulness (3)'" , "entertainment" , "Light-hearted pleasure" , "Enjoyment" , "Light-hearted amusement, jollity" .)